M - 3

External Marks: 60 L T P
Internal Marks: 40 3 1 -
Total Marks: 100
PREREQUISITES: Calculus of two variables and exposure to mathematics-I and
Mathematics - II.
OBJECTIVES:
To teach Engineering Mathematics to the students.
COURSE CONTENTS:
Review of the prerequisites such as limits of sequences and functions. Continuity,
uniform continuity and differentiability. Rolls theorem, mean value theorems and
Taylor's theorem. Newton method for approximate solution Riemann integral and the
fundamental theorem of integral calculus. Approximate integration. Applications to
length area, volume, surface area of revolution, Moments, centers of Mass and Gravity.
Repeated and multiple integrals with applications to volume, surface area, moments of
inertia etc. Analytic functions, Cauchy-Riemann equations, Laplace equation, elementary
functions, Cauchy's integral theorem(Proof by using Greens theorem), Cauchy's integral
formula, Taylor series and Laurent series. [33%
Residues and applications to evaluating real improper integrals and inverse Laplace
transforms. Conformal mapping, linear fractional transformations. [17%]
Boundary value problems involving partial differential equations such as wave equation,
heat equation, Laplace equations . Solutions by the method of separation of variables and
by Fourier and Laplace transforms. [33%]
Numerical Methods for ODEs and PDEs. [17%]